A007583 -id:A007583 - cp's OEIS frontend

A350717 a(n) = 4*a(n-1) - n - 1, for n > 0, a(0) = 1.

1, 2, 5, 16, 59, 230, 913, 3644, 14567, 58258, 233021, 932072, 3728275, 14913086, 59652329, 238609300, 954437183, 3817748714, 15270994837, 61083979328, 244335917291, 977343669142, 3909374676545, 15637498706156, 62549994824599, 250199979298370, 1000799917193453, 4003199668773784

Offset: 0

Paul Curtz, Feb 03 2022

Last digit (using 0 to 9) is of period 10: repeat [1, 2, 5, 6, 9, 0, 3, 4, 7, 8].

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Cf. A007583 (first differences), A014825, A160156.

LinearRecurrence[{6, -9, 4}, {1, 2, 5}, 28] (* Amiram Eldar, Feb 03 2022 *)

a(n) = if (n, 4*a(n-1) - n - 1, 1); \\ Michel Marcus, Feb 03 2022

print([(2**(2*n+1) + 3*n + 7)//9 for n in range(30)])
# Gennady Eremin, Feb 05 2022

a(n) = (2^(2*n+1) + 3*n + 7)/9.
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3), n >= 3.
a(n) = a(n-1) + A007583(n-1).
a(n) = 2*a(n-1) + A014825(n-1).
G.f.: (-2*x^2 + 4*x - 1)/((x - 1)^2*(4*x - 1)). - Thomas Scheuerle, Feb 03 2022
a(n) = -1 + 5*a(n-1) - 4*a(n-2), n >= 2.
a(n) = 1 + A160156(n-1), n >= 1.

More terms from Michel Marcus, Feb 03 2022

A360967 Array T(n,m) = (2^(m(2n+1))+1)/(2^m+1) read by antidiagonals.

Original entry on oeis.org

3, 13, 11, 57, 205, 43, 241, 3641, 3277, 171, 993, 61681, 233017, 52429, 683, 4033, 1016801, 15790321, 14913081, 838861, 2731, 16257, 16519105, 1041204193, 4042322161, 954437177, 13421773, 10923, 65281, 266354561, 67662254017, 1066193093601, 1034834473201, 61083979321, 214748365

Offset: 1

R. J. Mathar, Feb 27 2023

			The array starts in row n=1 and column n=1 as
      3      13      57     241
     11     205    3641   61681
     43    3277  233017 15790321
    171   52429 14913081 4042322161

Quynh Nguyen, Jean Pedersen, and Hien T. Vu, New Integer Sequences Arising From 3-Period Folding Numbers, JIS vol 19 (2016) #16.3.1 table 3

Cf. A007583 (col 1), A299960 (col 2).

cp's OEIS Frontend

A350717 a(n) = 4*a(n-1) - n - 1, for n > 0, a(0) = 1.

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A360967 Array T(n,m) = (2^(m(2n+1))+1)/(2^m+1) read by antidiagonals.

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cp's OEIS Frontend

A350717 a(n) = 4*a(n-1) - n - 1, for n > 0, a(0) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

Extensions

A360967 Array T(n,m) = (2^(m*(2*n+1))+1)/(2^m+1) read by antidiagonals.

Views

Author

Keywords

Examples

Links

Crossrefs

A360967 Array T(n,m) = (2^(m(2n+1))+1)/(2^m+1) read by antidiagonals.